
nötig
necessary
Required or necessary in order to achieve a specific goal or fulfill a condition.
Für die Einreise ist ein gültiger Reisepass nötig.
A valid passport is necessary for entry.
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necessary
Required or necessary in order to achieve a specific goal or fulfill a condition.
Für die Einreise ist ein gültiger Reisepass nötig.
A valid passport is necessary for entry.

to badly need something
A colloquial expression indicating that someone urgently needs something or strongly displays a certain behavior, often with a slightly negative or mocking connotation.
Nach der anstrengenden Woche habe ich eine Pause dringend nötig.
After the exhausting week, I badly need a break.
The adjective 'nötig' (necessary) is closely related to the noun 'die Not' (need/distress). 'Not' means a difficult situation or a shortage. Something that is 'nötig' (necessary) therefore helps you get out of a difficult situation or remedy a shortage.
Wir müssen sparen, weil das Geld knapp ist und jeder Euro nötig ist.
We have to save money because funds are tight and every euro is necessary.
'Nötig' (necessary) is very often used in impersonal sentences with 'es' (it). The constructions 'es ist nötig, dass ...' (it is necessary that ...) or 'es ist nötig, ... zu ...' (it is necessary to ...) are typical for expressing necessity.
Es ist nötig, das Formular bis morgen auszufüllen.
It is necessary to fill out the form by tomorrow.
When you want to state the purpose or condition for which something is necessary, use the preposition 'für' (for) followed by the accusative.
Für diesen Job sind gute Sprachkenntnisse nötig.
Good language skills are necessary for this job.
The colloquial expression 'etwas nötig haben' (to badly need something) follows a fixed pattern: the person is the subject, followed by 'haben' (to have), the object in the accusative, and 'nötig' (necessary). It is often intensified by adverbs such as 'dringend' (urgently/badly) or 'wirklich' (really).
Du siehst müde aus, du hast eine Pause wirklich nötig.
You look tired; you really need a break.
to need
Brauchen and etwas nötig haben can both express that someone urgently needs something. Brauchen is neutral and common in everyday speech, while nötig haben as a fixed expression sounds more emphatic and can sound mocking or critical depending on the situation. Brauchen is usually suitable for a normal statement; nötig haben can fit when expressing strong criticism.

Nach dem langen Lauf hast du dringend ein Glas Wasser nötig.
After the long run, you are badly in need of a glass of water.
Nach dem langen Lauf brauchst du dringend ein Glas Wasser.
After the long run, you urgently need a glass of water.